Impeller blade for axial flow fan having counter-rotating impellers

ABSTRACT

Method for determining the camber line and thickness distribution for blades used in a cooling fan with counter-rotating impellers. The camber lines and thickness distributions for the blades of each of the impellers are determined through use of Bezier curves and chosen to reduce boundary layer separation of airflow across the blades. The Bezier control points are altered to produce a set of distributions of the camber lines and thickness distributions, and the most favorable set is found with increased cooling efficiency.

This application is a continuation of U.S. application Ser. No.09/911,281 filed on Jul. 23, 2001, now Pat. No. 6,565,334, which was acontinuation-in part of U.S. application Ser. No. 09/624,583 filed onJul. 24, 2000, now U.S. Pat. No. 6,457,953, which was a continuation ofU.S. application Ser. No. 09/118,843 filed on Jul. 20, 1998, now Pat.No. 6,129,528.

FIELD OF THE INVENTION

The present invention relates to an axial flow fan, and moreparticularly to a multiple impeller arrangement with coaxial impellersthat rotate in opposite directions. The multiple impellercounter-rotating axial flow fan of the present invention is especiallysuitable for use in cooling electronic components.

BACKGROUND OF THE INVENTION

A conventional axial flow fan is generally composed of a driving motor,a cylindrical central hub section mounted on a motor shaft attached tothe driving motor, a plurality of blades affixed to the hub, and ahousing for encasing the fan or impeller, used herein as equivalentterms. Each of the blades extends radially outward from the central hubsection of the fan. The motor shaft is attached to the hub section at acentral aperture and thus the hub section may be rotated by the drivingmotor via the motor shaft. In such an arrangement, the hub sectiontogether with the blades are rotated by the motor about an axis of theouter casing in order to force air flow from an inlet area to an outletarea of the fan. The blades of the fan are air foils configured so as tomake the blades generate a force in the opposite direction of theblade's direction of rotation and an air flow that is perpendicular tothe blade's direction of rotation.

Axial flow fans such as Model No. 5920 produced by IMC MagneticsCorporation, the assignee of the present application, are known whichutilize a unipolar winding employing a four pole motor where only two ofthe windings are ON at a time. These fans employ circuitry includingcircuit elements of a substantial size, such as an inductor to reducethe starting current, transistors large enough to handle the powerlevels, and large clamping diodes needed to protect the transistors.Such axial flow fans cannot handle input voltages in the range of57V-64V, are limited to a maximum input voltage of about 56V, and aremore typically operated at an input voltage of about 48V.

Model No. 5920 measures two inches in axial width due to both the largesize of the diodes, inductors, and transistors used, as well as thenumber of turns required for a unipolar winding. Furthermore, the axialwidth of Model No. 5920 is attributed to its 5 blades wherein each bladeis characterized by a symmetrical cross-section approximately describedas curved flat plates. As such, these blades are not aerodynamicallyefficient and thus require a larger chord length to meet the performancerequirements forcing the dimensions of Model No. 5920 to a two inchaxial width.

With the continual increase in the density and load-carrying capabilityof electronic components on circuit boards, and the consequentialincrease in heating problems resulting therefrom, axial flow fans areincreasingly being used in an effort to combat such heating problems.During the design of such axial flow fans, it is important to make themas small and as cost-effective as possible while maintaining, or evenincreasing, their ability to cool electronic components. In particular,it is important to reduce the overall size of such a fan as much aspossible. For example, the two inches axial width of Model No. 5920 iswider than optimal for use as an axial flow fan for cooling electroniccomponents. Thus, it is desirable to reduce its size while maintainingits performance parameters and design constraints.

One method to reduce the overall size of such a fan is to eliminatelarge electronic components and reduce the size of other componentswhile maintaining performance parameters and design constraints. Forinstance, the housing of the axial flow fan may be utilized as a heatsink to reduce the axial width of the fan by eliminating the need for aseparate heat sink.

In addition, in order to reduce the overall size of an axial flow fan,it is desirable to utilize narrow chord blades. However, the use of suchnarrow chord blades results in decreased performance, particularly adecrease in the fan pressure and air flow. These decreases inperformance must be offset by varying the design parameters. It is knownthat, among other factors, the chord length, camber angle, staggerangle, and the cross-sectional shape of the blades are possible factorsaffecting the performance of the fan. In addition, it is known that byvarying the work distribution along a blade's span, the chord length maybe varied along the blade span while maintaining performance parameters.

In theory, the larger the camber angle, the greater the lift force undera constant angle of attack. However, if the camber angle is too largethe blade may stall, resulting in a decrease in performance and anincrease in noise signature. Consequently, the camber angle must bedesigned to the proper value.

By way of a further example, a decrease in the work distribution at aradial location will allow for a decrease in chord length with aresultant decrease in velocity exiting the blade at that radiallocation. Thus, it is desirable to minimize the work distribution at thehub section (root of the blade), since this affects axial width, and tomaximize the work distribution at the tip of the blade to deliver thegreatest blade exit velocity at the tip. Such an approach was disclosedin U.S. Pat. No. 5,320,493. However, this approach may lead to anintolerable increase in the noise signature of the fan due to theincrease in tip velocity exiting the blade as well as an increase inturbulent air exiting the tip of the blades. Thus, it is desirable tolocate the maximum work distribution at some favorable location betweenthe root portion and the tip portion.

Furthermore, the cross-sectional shape of the blade affects its velocitydistribution. Circular arc profiles, such as NACA series 65 airfoils,exhibit a velocity profile which results in a rapid decrease in thevelocity along the suction surface at the trailing edge of the blade.Such a large deceleration gradient results in a more unstable boundarylayer, promoting boundary layer separation and hence resulting in lossof lift and greater turbulent air exiting the blade. Thus, the velocityprofile of the cross-sectional airfoil must be designed so that afavorable velocity profile is achieved.

Various prior U.S. patents had been developed in this field. Forexample, U.S. Pat. No. 4,971,520, U.S. Pat. No. 4,569,631, U.S. Pat. No.5,244,347, U.S. Pat. No. 5,326,225, U.S. Pat. No. 5,513,951, U.S. Pat.No. 5,320,493, U.S. Pat. No. 5,181,830, U.S. Pat. No. 5,273,400, U.S.Pat. No. 2,811,303, and U.S. Pat. No. 5,730,483 disclose axial flowfans. However, the fans disclosed in these patents have not effectivelycombined the above parameters to overcome the problems described above.In particular no invention discloses a family of airfoil profiles or ablade which delivers the performance of the present invention whilereducing the axial width of the fan. Nor does any invention disclose useof such optimized blades in a multiple impeller counter-rotatingarrangement to further exploit the reduced width of each impellerindividually and to result in a fan having reduced overall size withimproved performance.

In the non-analogous field of aircraft rotors, the use of multiplecoaxial rotors, as shown in U.S. Pat. No. 3,127,093 to Sudrow, is known.The Sudrow Patent discloses a “Ducted Sustaining Rotor for Aircraft”which utilizes two sets of coaxial rotors, each of which has a pluralityof air foils configured to create lift. These rotors are mounted onmotor shafts which are capable of spinning in opposite directions. Suchcounter-rotating arrangements have been utilized to reduce torque, toreduce axial air flow and to reduce vibration and noise.

Unlike the air foils attached to aircraft rotors, the air foils attachedto fan rotors are configured to create air flow. Conventional theorypredicts that two identical axial flow fans operating in series in afree flow environment, where there is not substantial downstream flowresistance, will not provide more air flow than one of the axial flowfans operating by itself. Conventional theory also predicts that twoidentical axial flow fans operating in series in a flow restrictedenvironment, where there is substantial downstream flow resistance, willprovide at most twice the air flow of a single fan operating by itself,where the maximum increase is only approached as down stream flowresistance becomes very large. Conventional theory further predicts thatplacing two otherwise identical axial flow fans in a counter-rotatingarrangement, by inverting the rotor of one such fan and rotating saidrotor in the opposite direction of the other fan's rotor, will providethe same amount of air flow as the fans would provide in a co-rotatingarrangement. Since using two fans doubles the cost and powerrequirements of using a single fan, convention theory does not supportthe use of relatively complicated and bulky counter-rotatingarrangements.

U.S. Pat. No. 2,313,413 to Weske discloses an axial flow fan that usesmultiple co-rotating impellers with interspersed fixed blades. U.S. Pat.No. 5,931,640 to Van Houten et al. discloses using two counter-rotatingfans with oppositely skewed blades for use as vehicle engine coolingfan. These patents disclose that such arrangements allow the fans todevelop the required air flows while operating at slower speeds. Thesepatents also teach that the disclosed arrangements reduce parasiticloses and provide improved acoustic properties.

SUMMARY OF THE INVENTION

No invention in the prior art discloses a multi-impeller, coaxial,counter-rotating fan that provides increases in airflow compared to asingle impeller fan beyond what is predicted by conventional theory. Noinvention in the prior art discloses a counter-rotating fan thatprovides more than twice the air flow into a pressurized environment asa co-rotating fan. No invention in the prior art discloses a combinationof the factors to formulate a blade which delivers the desiredperformance while reducing the overall size to that of the presentinvention. In addition, no invention in the prior art discloses the useof such optimized blades in making dual impeller, coaxial,counter-rotating fan.

Through experimentation, it has been shown that a fan withcounter-rotating impellers employing the improved blade design describedherein will provide increases in air-flow as compared to a fan with asingle impeller that are substantially greater than the increasespredicted by conventional theory. In addition, it has been shown that afan with counter-rotating impellers employing the improved blade designdescribed herein will provide more than twice the air flow into apressurized environment as an otherwise identical fan with co-rotatingimpellers. Accordingly, it is an object of this invention to provide amultiple impeller axial flow fan in which the impellers aresubstantially coaxial and counter-rotating, with substantially improvedperformance parameters.

It is an additional object of the invention to provide a bladeincorporating a family of airfoil sections capable of reducing the axialwidth of an axial flow fan while maintaining performance parameters anddesign constraints.

It is yet another object of the invention to provide a bladeincorporating a family of airfoil sections which allow for the reductionof the axial width of an axial fan while locating the maximum workdistribution between the root portion and the tip portion of the blade.

It is yet another object of the invention to provide a bladeincorporating a family of airfoil sections that allow for the reductionof the overall size of an axial fan while maintaining a favorablevelocity profile over the suction side of the blade.

It is yet another object of the invention to provide a counter-rotatingimpeller arrangement that provides an increase in axial air flow whichis substantially greater than that predicted using theoretical models.

It is yet another object of the invention to provide a counter-rotatingimpeller arrangement that provides more than twice the air flow into apressurized environment as an otherwise identical co-rotating impellerarrangement.

It is yet another object of the invention to exploit the reduction ofwidth of the axial fans by utilizing same to make a multiple,counter-rotating impeller arrangement which provides an increase inaxial air flow feasible given certain design constraints of electricfans for use in cooling electronic components.

These and other objects are realized by an axial flow fan structure thatincludes at least two coaxial rotor assemblies, where each of the rotorassemblies further includes an impeller with a plurality of blades; andwhere at least one of said rotor assemblies is configured such that itrotates in a direction opposite to the first of said rotor assemblies;and where the blades on each of the rotor assemblies are configured sucheach impeller forces air in the same axial direction as the otherimpellers.

These and other objects are further realized by providing said impellerswith blades having the following characteristics: a root portion; a tipportion; a leading edge; a trailing edge; the blade having across-sectional shape, taken anywhere along a radius of the blade,characterized by a maximum thickness located substantially constantlybetween about 19% chord to about 20% chord and a maximum camber locatedsubstantially constantly between about 45% chord to about 46% chord.

It has been experimentally determined that the acoustic properties of adual impeller counter-rotating fan can be improved by having a differentnumber of blades on the upstream impeller than are on the downstreamimpeller. In a preferred embodiment, the upstream impeller consists ofthirteen radially extending blades coupled to a circular band and thedownstream impeller consists of eleven circumferentially spaced radiallyextending blades coupled to a circular band.

It has further been determined that air flow is optimized when saidmultiple counter-rotating impellers are located in a conically shapedhosing. The diameter of the second impeller may be greater than thediameter of the first impeller.

These and other objects, features, and advantages of the presentinvention will become more apparent in light of the following detaileddescription and accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be more easily understood with reference tothe following drawings.

FIG. 1 is an exploded perspective view of a single impeller axial flowfan.

FIG. 2 is a cross-sectional assembled view thereof.

FIG. 3 is an exploded perspective view of the stator assembly.

FIG. 4 is a top view of the printed circuit board base 52.

FIG. 5 is a top view of the stator core and winding.

FIG. 6(a) is a graphical representation of Flow (ft³/min.) vs. StaticPressure (inches of H₂O) for a single impeller axial flow fan.

FIG. 6(b) is a graphical representation of Flow (ft³/min.) vs. StaticPressure (inches of H₂O) for the following four separate axial flowfans: (A) a single impeller axial flow fan with normal rotation andnormally pitched blades; (B) a single impeller axial flow fan withreverse rotation and reverse pitched blades; (C) a two impellerco-rotating axial flow fan, where both impellers have normal rotationand normally pitched blades; and (D), in accordance with the presentinvention, a two impeller counter rotating axial flow fan, where oneimpeller has normal rotation and normally pitched blades and the otherimpeller has reverse rotation and reverse pitched blades.

FIG. 7(a) is a cross-sectional view of a standard impeller blade showingthe flow of air over the surfaces of the blade caused by the blademotion resulting from rotating the impeller.

FIG. 7(b) is a three-dimensional view of a single impeller axial flowfan showing the axial flow of air output by the fan as well as theradial (swirling) air flow created by rotating the impeller.

FIG. 7(c) is an idealized cross-sectional view of a single impelleraxial flow fan employing stator assemblies to remove the radialcomponent of the downstream air flow.

FIG. 7(d) is an idealized cross-sectional view of a two impeller counterrotating axial flow fan embodying the present invention, wherein theradial air flow imparted by the first impeller is removed by the secondimpeller.

FIG. 7(e) is an idealized cross-sectional view of a two impeller counterrotating axial flow fan having a conically shaped hosing.

FIG. 8 is a cross-sectional view of a blade in accordance with thepresent invention;

FIG. 9A is a frontal view of a blade in accordance with the presentinvention;

FIG. 9B is a side view of a blade in accordance with the presentinvention;

FIG. 10 is a three-dimensional view of a blade in accordance with thepresent invention;

FIG. 11 is a definitional diagram of the coordinate system utilized inthe description of the blades employed by the present invention;

FIG. 12 is a comparison of a graphical representation of a favorableblade surface velocity distribution near design conditions in accordancewith the present invention as compared to an unfavorable blade surfacevelocity distribution;

FIGS. 13A-C are tabular representations of the optimized normalizedBezier control points for the five airfoil sections of the preferredembodiment in accordance with the present invention;

FIG. 14 is a graphical representation of the camber line distribution atthe root portion of the preferred embodiment in accordance with thepresent invention along with the associated optimized normalized Beziercontrol points;

FIG. 15 is a graphical representation of the normal thicknessdistribution at the root portion of the preferred embodiment inaccordance with the present invention along with the associatedoptimized normalized Bezier control points;

FIG. 16 is a graphical representation of the normalized workdistribution of the preferred embodiment in accordance with the presentinvention;

FIG. 17 is a graphical representation of the camber line distribution ofthe five airfoil sections of the preferred embodiment in accordance withthe present invention;

FIG. 18 is a graphical representation of the thickness distribution ofthe five airfoil sections of the preferred embodiment in accordance withthe present invention;

FIG. 19 is a graphical representation of the normalized profiles of thefive airfoil sections of the blades of the preferred embodiment inaccordance with the present invention;

FIG. 20 is a tabular representation of the optimized values describingthe five airfoil sections of the preferred embodiment in accordance withthe present invention; and

FIGS. 21A-E are tabular representations of the normalized surfacecoordinates of the preferred embodiment in accordance with the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

General Structure of the Axial Flow Fan

A description of a preferred embodiment of the present invention willnow be given. Referring now to the drawings, and in particular to FIGS.1 and 2, wherein illustrated is an axial flow fan 100, comprising animpeller 10, for generating air flow when rotated, a yoke 20 mounted inimpeller 10, a shaft 30 coupled to yoke 20, a permanent magnet 40mounted in yoke 20, a stator assembly 50, a fan housing 70, aninsulation sheet 60 for electrically insulating the base within statorassembly 50 from fan housing 70, and bearings and mounting hardware 80which serve to secure the shaft 30 to housing 70 while allowing yoke 20and magnet 40 to freely rotate, thereby rotating impeller 10. Theimpeller 10 comprises a plurality of blades 11 equally spaced andcircumferentially mounted on circular band 12. The permanent magnet 40mounted in yoke 20, when combined with stator assembly 50, forms anelectrical motor which turns impeller 10 when a voltage is applied to anexciting circuit on the printed circuit board within stator assembly 50.The construction of stator assembly 50 is fully described in co-pendingand co-owned patent application Ser. No. 09/119,221 entitled “StatorMounting Method and Apparatus for a Motor,” which was filed on Jul. 20,1998, and which is incorporated herein by reference.

As shown in FIG. 7(d), the counter rotating fan of the preferredembodiment is comprised of a first single impeller axial flow fan asdescribed in the preceding paragraph and a second single impeller axialflow fan contained within a single housing. The input of the secondsingle impeller axial flow fan is connected to the output of the firstsingle impeller axial flow fan. In addition, the second single impelleraxial flow fan has an impeller that rotates in the reverse directioncompared to the direction of rotation of the impeller contained in thefirst single impeller axial flow fan and the second single impelleraxial flow fan has blades that are oppositely pitched as compared to theblades of the first single impeller axial flow fan.

In the preferred embodiment, the first impeller has thirteen blades andthe second impeller has eleven blades. In addition, the second impellercan be made slightly larger than the first impeller (i.e. with a longerdiameter) and the common housing can be in the shape of a cone with adiameter that expands from the input of the first impeller to the outputof the second impeller as shown in FIG. 7(e).

FIG. 3 depicts the stator assembly 50, comprising a base 52, fourinsulating pins 54, a stator core 56 and windings 58. In the preferredembodiment, base 52 is a printed circuit board including the circuitryfor exciting and operating the motor.

The base 52 as shown in FIG. 4 is a printed circuit board which hasmounted thereon the circuitry for operating the motor. The voltageregulator 57 permits use of an input voltage in the range of about 28Vto 64V, a greater range than in other fans such as the Model No. 5920fan mentioned in the section above entitled “Background of theInvention”. The input and output voltages of the voltage regulator aredifferent. The voltage regulator adjusts the voltage at the output to beappropriate for the IC circuitry on the output side of the voltageregulator. Delivering low voltages at the output of the voltageregulator to all resistors, transistors, diodes, and capacitors permitsthe use of small components reducing the size of the circuitry so thatit may be employed in a fan of a reduced width. In the preferredembodiment there is no need for the large clamping diodes such as PartNo. V03C manufactured by Hitachi employed in the Model No. 5920 axialflow fan. Four large transistors such as Part Nos. 25B1203-5manufactured by Sanyo employed in the circuitry of the Model No. 5920fan in order to handle the heat and power of the high voltage levels areeliminated in the invention. The preferred embodiment employs transistorswitches in the ICs 61 and 62 which operate on the reduced voltage levelof the output of the voltage regulator. Further, the inductor Part No.6308-R8151 manufactured by Minebea in the Model No. 5920 axial fan iseliminated in the invention. Accordingly, the finished circuit board ofthe preferred embodiment is of reduced width when compared to earliercircuit boards such as the circuit board for the Model No. 5920.Further, an axial flow fan with reduced width is achieved.

The preferred embodiment eliminates the need for large circuitcomponents including clamping diodes and transistors by employing avoltage regulator 57. The use of the voltage regulator to step down theinput voltage generates heat across the voltage regulator which must bedissipated. The housing 70 of the fan functions as a heat sink. Use ofthe housing 70 as the heat sink eliminates the need for a resistor ofsignificant size for use as the heat sink for the voltage regulator.Since the housing 70 functions as a heat sink as well as an enclosure, astandard heat compound which is a heat sinking thermo-conductiveadhesive such as Loctite® Thermally-Conductive Adhesive 3873 is used totransfer the heat from the voltage regulator 57 to the metal housing 70.Alternatively, or additionally, a pin may be used to secure the voltageregulator IC 57 to the housing. The pin functions to temporarily securethe voltage regulator during the curing of the heat compound.Accordingly, a fan of reduced width is achieved.

In practice, when combined with the blade design discussed below, asingle impeller axial flow fan having a one inch thickness and havingthe same air flow output as the Model 5920 IMC Magnetic Corp. axial flowfan (which is two inches thick) is achieved by implementing the abovedescribed improvements and a two impeller counter rotating axial flowfan having a two inch thickness and having the improved air flowcharacteristics of the present invention is achieved by implementing theabove described improvements.

Parameters of the Blade Structure

FIG. 8 is a cross-sectional view of one of the blades 11 of thepreferred embodiment of the present invention and it depicts theparameters which define, in part, the cross-sectional shape 14 of theblades 11 of the present invention. Each cross-section has a leadingedge 16, trailing edge 18, upper surface 22, and lower surface 24. Thecross-section may be further defined by the stagger angle 26, camberangle 28, chord line 32, chord length 34, camber line 36, and thickness(t) 38.

Referring now to FIGS. 9A and 9B, blades 11 of the preferred embodimentare constructed by radially and axially stacking and blending thecross-sections 14 in order to form a three-dimensional blade. FIG. 9A isa frontal view of blades 11 while FIG. 9B is a side view of blades 11.Thus, the view of FIG. 9B is a rotated 90 degrees from the view of FIG.9A. The blade has a root portion 42 and a tip portion 44. The rootportion 42 is coterminous with the circumference of circular band 12(FIG. 1). Each airfoil section 14 of blade 11 is identified with respectto the radius which originates from the center of circular band 12 andextends radially outward as depicted in FIG. 9B. The location of eachairfoil section 14 is defined by r/r_(tip) which is the ratio of theradial location of the particular cross-section 14 (r) divided by theradius of the airfoil section at the tip portion 14 (r_(tip)) in FIGS.9A and 9B as shown.

The Circumferential Stacking axis is defined by an axis that intersectsthe leading edge 16 of cross-section 14 located at the root portion 42and extends in the circumferential direction. Circumferential Stackingdistance is defined by the distance between the leading edge 16 of anairfoil cross-section 14 and the Circumferential Stacking axis. TheAxial Stacking axis is defined by an axis that intersects the leadingedge 16 of the cross-section 14 located at the root portion 42 andextends in the axial direction. Axial Stacking distance is defined bythe distance between the leading edge 16 of an airfoil cross-section 14and the Axial Stacking axis. Once the cross sections 14 are stacked, athree-dimensional blade 11 results as depicted in FIG. 10. FIG. 11 is adefinitional diagram showing a cross-section of a randomly chosen bladewhich presents the coordinate axes used to define blades 11 andcross-sectional shapes 14 of the present invention.

The blades of the present invention were designed according to thefollowing method. A series of fan performance parameters and designconstraints to be satisfied by the single impeller axial flow fan 100and accompanying blades 11 were set. Fan performance parameters includevolumetric flow rate at the free air condition defined in cubic feet perminute (ft³/min), shaft speed (rpm), and inlet air density in pounds percubic feet (lbs/ft³). Design constraints include fan size (includingaxial width), fan weight, motor input power, and acoustic noisesignature. These performance parameters and design constraints were setas: volumetric flow rate of 240 ft³/min, shaft speed of 3400 rpm, andinlet air density of 0.075 lbs/ft³, and axial width fan size of 1 inch.Although these are the optimum requirements, satisfactory results may beobtained for a volumetric flow rate of 225 to 255 ft³/min and a shaftspeed of 3200 to 3600 rpm. Among these parameters and constraints themost important are the volumetric flow rate and axial width fan size.

For the aerodynamic design, a multi-streamline, indirect method was usedto determine the optimum values of chord length 34, camber angle 28, andstagger angle 26 which are capable of delivering the specified fanperformance parameters and satisfying the stated design constraints.Based on experience, the desired work distribution was selected. Workdistribution is defined as the angular momentum distribution of the airflow at the outlet of the impeller 10 (trailing edge 18 of cross-section14). The work distribution affects the size of the chord length 34.Finally, based on experience, the number of impeller blades wereselected to optimize the flow output and fan width.

The next step was to determine the camber line and thicknessdistributions. These distributions were determined through use of Beziercurves, an example of such use is referenced in Casey, “A ComputationalGeometry for the Blades and Internal Flow Channels of CentrifugalCompressors”, ASME 82-GT-155. This method determines the distributionsin camber line and thickness in the following parametric form:${F(u)} = {\sum\limits_{k = O}^{k = n}{f_{k}{B_{k}^{n}(u)}}}$Wherein:

F(u) represents the solution of the Bezier curve which, in this instanceis separately applied to determine the camber line x and y coordinates${B_{k}^{n}(u)} = {\begin{pmatrix}n \\k\end{pmatrix}{u^{k}( {1 - u} )}^{n - k}}$as well as the thickness distribution;

-   -   u is a parameter that varies linearly between 0 and 1, (u=0 at        the leading edge 16 and u=1 at the trailing edge 18);    -   f_(k) is a one-dimensional array of Bezier control points;    -   B_(k) ^(n)(u) is the Bernstein polynomial of degree n;    -   n+1 is the number of Bezier control points; and        $\quad\begin{pmatrix}        n \\        k        \end{pmatrix}$    -    are the binomial coefficients as defined in CRC Standard        Mathematical Tables, 22nd Ed., 1974, p. 627.

n was chosen to be 18 so that the resultant Bezier equations were an18th degree polynomial which resulted in 19 control points. Such aselection affords much more precision in optimizing the cross-sectionalshapes 14 of the blades 11 than a lower order polynomial. The resultingequations for the Bezier curves are: $\begin{matrix}\begin{matrix}{{X_{c}(u)} = {{{A_{0}( {1 - u} )}^{18}x_{0}} + {A_{1}{u( {1 - u} )}^{17}x_{1}} + {A_{2}{u^{2}( {1 - u} )}^{16}x_{2}} +}} \\{{A_{3}{u^{3}( {1 - u} )}^{15}x_{3}} + {A_{4}{u^{4}( {1 - u} )}^{14}x_{4}} + {A_{5}{u^{5}( {1 - u} )}^{13}x_{5}} +} \\{{A_{6}{u^{6}( {1 - u} )}^{12}x_{6}} + {A_{7}{u^{7}( {1 - u} )}^{11}x_{7}} + {A_{8}{u^{8}( {1 - u} )}^{10}x_{8}} +} \\{{A_{9}{u^{9}( {1 - u} )}^{9}x_{9}} + {A_{10}{u^{10}( {1 - u} )}^{8}x_{10}} + {A_{11}{u^{11}( {1 - u} )}^{7}x_{11}} +} \\{{A_{12}{u^{12}( {1 - u} )}^{6}x_{12}} + {A_{13}{u^{13}( {1 - u} )}^{5}x_{13}} + {A_{14}{u^{14}( {1 - u} )}^{4}x_{14}} +} \\{{A_{15}{u^{15}( {1 - u} )}^{3}x_{15}} + {A_{16}{u^{16}( {1 - u} )}^{2}x_{16}} + {A_{17}{u^{17}( {1 - u} )}x_{17}} +} \\{A_{18}u^{18}x_{18}}\end{matrix} \\\begin{matrix}{{Y_{c}(u)} = {{{A_{0}( {1 - u} )}^{18}y_{0}} + {A_{1}{u( {1 - u} )}^{17}y_{1}} + {A_{2}{u^{2}( {1 - u} )}^{16}y_{2}} +}} \\{{A_{3}{u^{3}( {1 - u} )}^{15}y_{3}} + {A_{4}{u^{4}( {1 - u} )}^{14}y_{4}} + {A_{5}{u^{5}( {1 - u} )}^{13}y_{5}} +} \\{{A_{6}{u^{6}( {1 - u} )}^{12}y_{6}} + {A_{7}{u^{7}( {1 - u} )}^{11}y_{7}} + {A_{8}{u^{8}( {1 - u} )}^{10}y_{8}} +} \\{{A_{9}{u^{9}( {1 - u} )}^{9}y_{9}} + {A_{10}{u^{10}( {1 - u} )}^{8}y_{10}} + {A_{11}{u^{11}( {1 - u} )}^{7}y_{11}} +} \\{{A_{12}{u^{12}( {1 - u} )}^{6}y_{12}} + {A_{13}{u^{13}( {1 - u} )}^{5}y_{13}} + {A_{14}{u^{14}( {1 - u} )}^{4}y_{14}} +} \\{{A_{15}{u^{15}( {1 - u} )}^{3}y_{15}} + {A_{16}{u^{16}( {1 - u} )}^{2}y_{16}} + {A_{17}{u^{17}( {1 - u} )}y_{17}} +} \\{A_{18}u^{18}y_{18}}\end{matrix} \\\begin{matrix}{{T_{n}(u)} = {{{A_{0}( {1 - u} )}^{18}t_{0}} + {A_{1}{u( {1 - u} )}^{17}t_{1}} + {A_{2}{u^{2}( {1 - u} )}^{16}t_{2}} +}} \\{{A_{3}{u^{3}( {1 - u} )}^{15}t_{3}} + {A_{4}{u^{4}( {1 - u} )}^{14}t_{4}} + {A_{5}{u^{5}( {1 - u} )}^{13}t_{5}} +} \\{{A_{6}{u^{6}( {1 - u} )}^{12}t_{6}} + {A_{7}{u^{7}( {1 - u} )}^{11}t_{7}} + {A_{8}{u^{8}( {1 - u} )}^{10}t_{8}} +} \\{{A_{9}{u^{9}( {1 - u} )}^{9}t_{9}} + {A_{10}{u^{10}( {1 - u} )}^{8}t_{10}} + {A_{11}{u^{11}( {1 - u} )}^{7}t_{11}} +} \\{{A_{12}{u^{12}( {1 - u} )}^{6}t_{12}} + {A_{13}{u^{13}( {1 - u} )}^{5}t_{13}} + {A_{14}{u^{14}( {1 - u} )}^{4}t_{14}} +} \\{{A_{15}{u^{15}( {1 - u} )}^{3}t_{15}} + {A_{16}{u^{16}( {1 - u} )}^{2}t_{16}} + {A_{17}{u^{17}( {1 - u} )}t_{17}} +} \\{A_{18}u^{18}t_{18}}\end{matrix}\end{matrix}$Wherein:

X_(c) is the x coordinate of the camber line normalized by the chordlength,

Y_(c) is the y coordinate of the camber line normalized by the chordlength,

T_(n) is the thickness distribution normalized by the chord length,

A₀ to A₁₈ are the Bernstein Polynomial Coefficients according to thefollowing values: $\quad\begin{matrix}{A_{0} = 1} & {A_{6} = 18564} & {{A_{12} = 18564}\quad} & {A_{18} = 1} \\{A_{1} = 18} & {A_{7} = 31824} & {A_{13} = 8568} & \quad \\{A_{2} = 153} & {A_{8} = 43758} & {A_{14} = 3060} & \quad \\{A_{3} = 816} & {A_{9} = 48620} & {A_{15} = 816} & \quad \\{A_{4} = 3060} & {A_{10} = 43758} & {A_{16} = 153} & \quad \\{{A_{5} = 8568}\quad} & {{A_{11} = 31824}\quad} & {A_{17} = 18} & \quad\end{matrix}$

and

x₀ to x₁₈ (hereinafter referred to as “x_(k)”) are the normalized xcoordinates of the Bezier control points;

y₀ to y₁₈ (hereinafter referred to as “y_(k)”) are the normalized ycoordinates of the Bezier control points; and

t₀ to t₁₈ (hereinafter referred to as “t_(k)”) are the normalizedthickness control points.

Based on experience, initial values of the Bezier control points x_(k),y_(k), and t_(k) were selected. With these control points, the aboveequations were solved for camber and thickness distributions.

Once the distributions along with the optimum chord length 34, camberangle 28, and stagger angle 26 were determined, an inviscid flowanalysis was utilized to determine the surface velocity distribution onthe suction (upper) side and the pressure (lower) side along with thework distribution of blade 11. The velocity distribution and resultingwork distribution were viewed by the designer to verify that the workdistribution profile is consistent with the initial design selection andalso to assure that a favorable velocity profile had been achieved.

A typical desirable blade surface velocity distribution is sought thatexhibits favorable deceleration gradients, favorable in the sense thatthe velocity distribution does not promote boundary layer separation andthereby weaken blade 11 performance. FIG. 12 is a comparison of agraphical representation of a favorable blade surface velocitydistribution near design conditions in accordance with the presentinvention (at r/r_(tip)=0.6459) as compared to an unfavorable bladesurface velocity distribution. A favorable work distribution is one thatlocates the maximum work distribution at a point somewhere between theroot portion and the tip portion.

After the initial iteration, since the resultant velocity distributionand work distribution were unfavorable or unsatisfactory to thedesigner, the Bezier control points were manually varied in order toachieve different camber and thickness distributions. Once again, thevelocity and work distributions were analyzed to determine if afavorable solution had been achieved. This process was repeated until afavorable solution was achieved. In the preferred embodiment, theoptimized normalized Bezier control points are shown in tabular form inFIGS. 13A-C.

These optimized Bezier control points along with the optimized camberdistribution and thickness distribution for the airfoil section 14located at the root portion 42 are graphically represented in FIGS. 14and 15. The work distribution is graphically represented in FIG. 16 forall five of the airfoil sections 14 of the preferred embodiment. As seenin FIG. 16, the maximum work distribution is located between the rootportion and the tip portion. The camber line and thickness distributionsfor all five of the airfoil sections 14 of the preferred embodiment areshown in FIGS. 17 and 18 along with a representation of thecross-sectional profile at r/r_(tip)=0.7908.

From the optimized camber line and thickness distributions, the bladesurface coordinates were determined in a manner similar to that used inthe NACA families of wing sections as referenced on pages 111-13 of“Theory of wing sections” by IRA H. ABBOTT and ALBERT E. VON DOENHOFFpublished in 1959 by the DOVER PUBLICATIONS, INC.

The blade surface coordinates are found from the chord line 32, camberline 36, and normal thickness distributions as follows:X _(UPPER) =X _(c) −Y _(t) SinY _(UPPER) =Y _(c) +Y _(t) Cos X _(LOWER) =X _(c) +Y _(t) SinY _(LOWER) =Y _(c) −Y _(t) CosWherein:

X_(UPPER), Y_(UPPER), X_(LOWER), and Y_(LOWER) are the coordinates ofthe upper (suction) surface 22 and lower (pressure) surface 24 of theblade, respectively;

X_(c) and Y_(c) are the coordinates of the camber line 36;

Y_(t) is one-half the thickness of the blade 11; and

Tan is the slope of the camber line 36 where Tan=dY_(c)/dX_(c).

The normalized cross-sectional profiles for the preferred embodiment areshown plotted in FIG. 19. FIGS. 21A-E are tabular representations ofsurface coordinates of the preferred embodiment in non-dimensionalvalues.

Once the desired cross-sections 14 are found at each radial location, athree-dimensional blade 11 is formed by stacking circumferentially andaxially each of the five cross-sections 14, with each cross-section 14offset from the root portion 42 by the prescribed stacking distance. Thefive cross-sections 14 are blended in a smooth and continuous manner.The resulting optimum values for the five cross-sectional profiles arepresented in FIG. 20. The key defining parameters are a maximumthickness located substantially constantly between about 19% chord toabout 20% chord and a maximum camber located substantially constantlybetween about 45% chord to about 46% chord. Although these are theoptimum range of values, there is an extended range of values which willsubstantially meet the performance parameters and design constraints ina satisfactory, although not optimum, manner. These values are a maximumthickness located substantially constantly between about 16% chord toabout 23% chord and a maximum camber located substantially constantlybetween 40% and 51% chord.

Also seen in FIG. 20 are other key defining parameters for eachcross-sectional profile such as the maximum thickness and maximum camberheight (both displayed in inches and as a percentage of the chord lengthat the particular radial station), camber angle, stagger angle, radius,chord length, and circumferential and axial stacking distances. Themaximum thickness in inches for each cross-sectional profile ischaracterized by a constant value. The maximum thickness as a percentageof chord length varies from a maximum value at the root portiondecreasing in value to a minimum value located substantially between 79%to about 90% of a radius measured from the center of the impeller to thetip portion followed by an increase in value to the tip portion of theblade. The maximum camber height, both in inches and as a percentage ofthe chord length at the particular radial station, varies from a maximumcamber height at the root portion continuously decreasing in maximumcamber height to the tip portion of the blade.

The camber angle is characterized by a maximum value at the root portioncontinuously decreasing in value to the tip portion of the blade. Thestagger angle, on the other hand, is characterized by a minimum value atthe root portion continuously increasing in value to the tip portion ofthe blade. In addition, the cross-sectional profile of blades 11 may bedescribed by its geometrical shape with the leading edge being similarto a parabola in shape, a convex upper surface, and a lower surfacewhich is convex towards the leading edge and concave towards thetrailing edge.

Other parameters in FIG. 20 include the aspect ratio and the solidity.The aspect ratio is defined as the length of the blade divided by thechord at the particular cross-section in dimensionless units. The lengthof the blade is defined as the radius at the tip portion (r_(tip)) minusthe radius at the root portion (r_(root)). The solidity is defined asthe chord length at the particular radial station divided by the bladespacing in dimensionless units. The blade spacing is the distancebetween adjacent blades at a given radius and is further defined bydividing 2πr by the number of blades. Finally, the normalized radius,normalized chord, and normalized circumferential and axial stackingdistances are presented in FIG. 20 which are all defined indimensionless units by dividing the value of the parameter at aparticular radius station by the maximum value of that parameter. Theblades discussed herein may be used in the counter-rotating impellerdiscussed below.

Counter-Rotating Impeller

The most important parameter in an electric fan of given physicaldimensions and power input being used to cool electronic components isair flow. The more air flow which can be caused to pass over theelectronic components, the more heat will be dissipated. Air flow isoften measured in cubic feet per minute (CFM).

When air impelled by a fan is not restricted in any way downstream ofthe fan, the condition is called free-air, i.e. the static-pressureresisting the flow from the fan is zero. When air is restricted, e.g. itis forced over a set of electronic components and out of the containersurrounding the electronic components, then a certain amount of staticpressure will build up. How much static pressure will build up given aspecific air flow depends upon many physical parameters including theconfiguration of the electronic components to be cooled, the size of thecontainer surrounding the electronic components and how the container isvented to the atmosphere. That is, a very complicated set of electroniccomponents in a small box with limited ventilation will result in arelatively high static pressure while a simple set of electroniccomponents in a larger and better ventilated container will result in arelatively low static pressure for the same amount of air flow.

Classical air flow theory predicts that placing two fans coaxially inseries with one another results in a minimal increase in air flow forfree-air, i.e. in the case where there is essentially no back-pressuredownstream of the fans. Classical theory also predicts that as the backpressure increases the air flow of the coaxial set of fans may increaseby a factor of up to 2 over the single fan case.

FIG. 6(a) is a graphical representation of Air flow (CFM) vs. StaticPressure (inches of H₂O) for a fan manufactured by IMC and designatedthe 5910 series tube-axial fan. As can be seen from FIG. 6(a), the airflow value for free-air condition is approximately 240 CFM while at astatic pressure value of approximately 0.6 inches of H₂O, the air flowis 0 CFM.

Tests were conducted with two coaxial IMC 5910 series tube axial fans.The fans were placed coaxially and adjacent to each other. Measurementsof flow vs. static pressure were taken for these fans rotating in thesame direction and counter-rotating (opposite directions). The resultsof these tests are shown at FIG. 6(b). As can be seen in FIG. 6(b),classical air flow theory is followed regarding the fans rotating intandem, i.e. there is only a marginal increase in air flow for afree-air condition which increases only gradually as the static pressureis increased.

The counter-rotating impeller structure in accordance with the inventionis shown in FIG. 7(d). The counter-rotating blades force air in the samedirection because the pitch of the second impeller is the opposite ofthat of the first impeller. As can be seen in FIG. 6(b), classical airflow theory fails to properly predict the air flow for a given staticpressure. Although for the free-air case, the increase in air flow isstill only marginal, the increase in air flow is more immediate anddrastic for the counter-rotating preferred embodiment of the invention.

The aerodynamic effects which may explain this marked increase in airflow efficiency are grouped into two major categories: profile drag andsecondary flow. Profile drag makes up everything from impeller bladeshape and surface finish, turbulent air created by the impeller, evendrag created by the blades. The turbulent air created by the impeller isshown in FIG. 7(a). Secondary flow consists of mainly swirling flow(radial velocity) and air flow losses due to the internal wall of thefan. An illustration of swirling flow is shown in FIG. 7(b). This flowis caused by the interaction of the air with the blades of the impellerand the constraining walls of the tube which encloses the impeller. Allof these aerodynamic effects reduce the efficiency of the fan.

“In theory”, i.e. without consideration of complicated aerodynamicfactors, fan efficiency is 100%. Taking into consideration allaerodynamic factors, the efficiency of the fan can be reduced to wellbelow 50%. In the case of the same-rotation test these effects areintensified. Inlet air is, in theory, laminar (free flowing with noturbulence). After the air leaves the first fan, it is turbulent andflows in a “corkscrew” fashion downstream. This turbulent air is now aninlet for another fan rotating in the same direction. The finaldownstream air corkscrews even more. These unwanted aerodynamic effectsseverely hurt the overall fan efficiency.

To maintain a high efficiency in an axial fan, a designer wants tominimize the aerodynamic effects as much as possible. Design constraintspermitting, the best configuration for an axial fan is: use pre-rotatingstators to change the direction of the inlet air into rotor blade, anduse straightening stators to correct the flow back into free stream flowas much as possible. Such an idealized configuration is illustrated atFIG. 7(c). Such an idealized structure will significantly minimize thesecondary flow effects and, therefore, keep aerodynamic efficiency (andoverall fan efficiency) at a higher level.

As shown in FIG. 7(d), the use of counter-rotating impellers of thepresent invention accomplishes the same effect as the idealizedstructure of FIG. 7(c). The laminar flow of air input to the firstimpeller is “pre-rotated” by the first impeller which increases bothaxial and radial (swirling) flows downstream. These flows are then“straightened” by the second impeller rotating coaxially in the oppositedirection. The second fan increases the axial flow further and regainsmost of the radial (swirling) flow otherwise lost in the system. Nowthat the swirling caused by the first impeller is all but canceled outby the second, aerodynamic efficiency is greater. This greaterefficiency helps improve total air flow of the system.

The invention further contemplates the method of locating Nsubstantially coaxial impellers within a housing, wherein N is aninteger; rotating at least one impeller in a direction opposite to thedirection of rotation of a first impeller of said N impellers; operatingthe impellers to force air in the same direction; and generating an airflow from the N impellers in the housing that is greater than N timesthe air flow of a single impeller, provided that the static pressure atthe fan output is greater than some minimum pressure. The staticpressure is dependent upon the characteristics of the specific fan,including the size of the fan. For example, the static pressure isapproximately 0.3 inches of water for a fan with two counter-rotatingimpeller and a diameter six inches.

FIG. 6(b) shows that when operating in an optimal pressure range, theair flow of two counter-rotating impellers can be substantially greaterthan twice the air flow of a single normal rotating impeller operatingin the same environment for some static pressure values, i.e. the samehousing for establishing the back pressure conditions. In addition, thecounter-rotating impellers of the invention, provide substantiallygreater air flow than the air flow generated by two impellers rotatingin the same direction as shown in FIG. 6(b).

The invention may include multiple substantially coaxial impellers. Atleast one impeller rotates in the opposite direction. Thus, there may beN impellers where N is an integer. If N is an even number half theimpellers may rotate in a first direction and half may rotate in theopposite direction. The direction of rotation may alternate betweenadjacent impellers. All the impellers may be identical, in which casethe total air flow is substantially greater than N times the air flowfor a single impeller operating in the same environment above, providedthat the static pressure at the output of the fan is greater than someminimum pressure. If the impellers are not identical, the total air flowis substantially greater then the sum of the air flow of each impellerof the N impellers operating in the same environment, provided that thestatic pressure at the output of the fan is greater than some minimumpressure.

The multiple impellers of the coaxial counter-rotating structure mayhave blades such as those of the IMC 5910 series or the blades describedabove in the section entitled “Parameters of the Blade Structures”.

The first and second impellers each have their own separate motor andthe stators of the motors are oppositely wound normal to generaterotation in opposite directions. Alternatively, the motors may share ashaft.

To summarize, the present invention provides an axial flow fan withnovel circuitry and housing, and a novel blade consisting of a pluralityof airfoil sections blended together which allow the axial width of anaxial flow fan to be reduced while maintaining the desired performanceparameters and design constraints. The present invention also disclosesa plurality of coaxial counter-rotating impellers with much greater airflow values at given static pressure values than would be expected underclassical theories. In addition, the blades enable a multiplicity ofcoaxial counter-rotating impellers to be exploited to their greatestpossible advantage despite design constraints regarding the dimensionalparameters for electric motors used in cooling electronic components.

Further, additional air flow or acoustic advantages can be achieved forthe counter-rotating axial flow fan of the present invention byimplementing one or more of the following design improvements:

-   -   attaching a different number of blades to the reverse rotating        impellers than are attached to the normal rotating        impellers(which reduces the noise signature of the fan);    -   determining the diameter of an impeller based upon the axial        location of that impeller within the fan such that the diameter        of an impeller near the outlet of the fan is greater than the        diameter of an impeller near the inlet of the fan (which        increases the airflow); and    -   placing the impellers into a cone shaped housing, where the        diameter of the conic sections increase from the inlet of the        fan to the outlet of the fan (as shown in FIG. 7(e) which        increases the airflow).

Now that the preferred embodiments of the present invention have beenshown and described in detail, various modifications and improvementsthereon will become readily apparent to those skilled in the art. Forexample, minor deviations from the disclosed values and approximationsof the disclosed equations are intended to be within the spirit of theinvention. Further, minor deviations or differences due to blending ofthe cross-sectional designs or due to different blending approaches areintended to be within the spirit and scope of the invention. A viableproduct may be obtained for substantially the same performanceparameters and design constraints, or where differences in theperformance parameters and design constraints have little commercialsignificance, by varying the methods of design in minor ways such aschoosing a different value for the number of control points, choosing adifferent value for the number of cross-sectional profiles, choosing adifferent value for the number of blades, defining the cross-sectionalprofiles by different radial distances, or choosing a different stackingdistance, stagger angle, camber angle, or chord length, where thedifferences in values are minor. The drawings and descriptions of thepreferred embodiments are made by way of example rather than to limitthe scope of the inventions, and they are intended to cover, within thespirit and scope of the inventions, all such changes and modificationsstated above.

1. A method for determining a first optimum camber line and thicknessdistribution in a first blade used in a first impeller and a secondoptimum camber line and thickness distribution in a second blade used ina second impeller, comprising the steps of: determining a series ofperformance parameters and design constraints for a counter rotating fancomprised of said first impeller and said second impeller; determining achord length, a camber angle, and a stagger angle for said first bladeand a chord length, a camber angle, and a stagger angle for said secondblade, utilizing Bezier curves to determine the optimum camber line andthickness distributions in said first blade and in said second blade. 2.The method of claim 1 wherein: one of the design constraints is thatsaid first blade is identical to said second blade except that in saidcounter rotating fan said second blade is oppositely pitched to saidfirst blade.
 3. A method for determining optimum camber line andthickness distributions in a first blade used in a first impeller and ina second blade used in a second impeller where said first blade and saidsecond blade each have a root portion, a tip portion, a leading edge anda trailing edge, comprising the steps of: determining a series of fanperformance parameters and design constraints for a counter rotating fancomprised of said first impeller and said second impeller; utilizingBezier curves to determine the appropriate camber line and thicknessdistributions according to the equation${F(u)} = {\sum\limits_{k = O}^{k = n}{f_{k}{B_{k}^{n}(u)}}}$ wherein:F(u) represents the solution of the Bezier curve; u is a parameter thatvaries linearly between 0 and 1, (u=0 at the leading edge and u=1 at thetrailing edge); f_(k) is a one-dimensional array of Bezier controlpoints; B_(k) ^(n)(u) is the Bernstein polynomial of degree n;${{B_{k}^{n}(u)} = {\begin{pmatrix}n \\k\end{pmatrix}{u^{k}( {1 - u} )}^{n - k}}};$ n+1 is the numberof Bezier control points; and $\quad\begin{pmatrix}n \\k\end{pmatrix}$  are the binomial coefficients as defined in CRC StandardMathematical Tables, 22nd Ed., 1974, p. 627; selecting initial values ofthe Bezier control points; separately applying F(u) to determine thecamber line x and y coordinates as well as the thickness distributions;conducting an inviscid flow analysis to determine a surface velocitydistribution and a work distribution for each of the resultantcamberline and thickness distributions; altering the Bezier controlpoints, acquiring different camber and thickness distributions, andrepeating the process until a favorable solution is achieved.
 4. Themethod disclosed in claim 3 wherein: the fan performance parametersinclude a volumetric flow rate, a shaft speed and inlet air density. 5.The method disclosed in claim 3 wherein: the design constraints includefan size, fan weight, motor input power, and acoustic noise signature.6. The method disclosed in claim 3 wherein: the fan performanceparameters include a volumetric flow rate, a shaft speed and inlet airdensity; and the design constraints include fan size, fan weight, motorinput power, and acoustic noise signature.
 7. The method disclosed inclaim 3 wherein: n is chosen to be 18 so that the resultant Bezierequations are an 18^(th) degree polynomial.
 8. The method disclosed inclaim 3 wherein: the surface velocity distribution does not promoteboundary layer separation.
 9. The method disclosed in claim 3 wherein:the work distributions locate the maximum work distribution at a pointbetween the root portion and the tip portion.